Least supported bases and local linear independence

1994 ◽  
Vol 67 (3) ◽  
pp. 289-301 ◽  
Author(s):  
J.M. Carnicer ◽  
J.M. Pe\~na
Keyword(s):  
Linear Independence ◽  
Local Linear ◽  
Local Linear Independence

scholarly journals On the local linear independence of translates of a box spline

1985 ◽  
Vol 82 (3) ◽  
pp. 243-263 ◽  
Author(s):  
Wolfgang Dahmen ◽  
Charles Micchelli
Keyword(s):  
Linear Independence ◽  
Local Linear ◽  
Box Spline ◽  
Local Linear Independence

Local linear independence of refinable vectors of functions

2000 ◽  
Vol 130 (4) ◽  
pp. 813-826 ◽  
Author(s):  
T. N. T. Goodman ◽  
R.-Q. Jia ◽  
D.-X. Zhou
Keyword(s):  
General Theory ◽  
Linear Independence ◽  
Nonlinear Approximation ◽  
Complete Characterization ◽  
Bounded Domains ◽  
Refinement Equation ◽  
Refinement Mask ◽  
Local Linear ◽  
Image Position ◽  
Local Linear Independence

This paper is devoted to a study of local linear independence of refinable vectors of functions. A vector of functions is said to be refinable if it satisfies the vector refinement equation where a is a finitely supported sequence of r × r matrices called the refinement mask. A complete characterization for the local linear independence of the shifts of ϕ1,…,ϕr is given strictly in terms of the mask. Several examples are provided to illustrate the general theory. This investigation is important for construction of wavelets on bounded domains and nonlinear approximation by wavelets.

A Local Linear Wavelet Neural Network Based on a Bayesian Design Method

2009 ◽  
Vol 129 (7) ◽  
pp. 1356-1362
Author(s):  
Kunikazu Kobayashi ◽  
Masanao Obayashi ◽  
Takashi Kuremoto
Keyword(s):  
Neural Network ◽  
Design Method ◽  
Wavelet Neural Network ◽  
Bayesian Design ◽  
Local Linear

Examples of theories of presheaf type

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Finite Groups ◽  
Linear Independence ◽  
Geometric Theory ◽  
Vector Spaces ◽  
Linear Orders ◽  
Locally Finite ◽  
Strong Unit ◽  
Locally Finite Groups ◽  
Simplicial Sets ◽  
Separable Extensions

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

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